An index to quantify an individual's scientific research output

Definition:

Adopting a linear model h=m*n, the m-parameter gives the estimated value of the h-index after n years of publishing, assuming that papers of similar quality are produced at a steady rate.

Interpretation:

However, a direct comparison of the h-indices is only possible for two individuals with the same scientific age n. Using the m-parameter and the linear model above, the h-indices of two individuals can be adjusted to the same n, although this may be inaccurate.

Based on typical values for h and m, the following interpretation (with large error bars) is proposed:

h-index: (for faculty at major research universities)

• 10≤h≤12: might be a typical value for advancement to tenure (associate professor)
• h≈18: advancement to full professor
• 15≤h≤20: fellowship in the American Physical Society might typically occur at this level
• h≥45: membership in the US National Academy of Sciences may typically be associated with such a value, except in exceptional circumstances.

m-parameter:

• m≈1: successful scientist
• m≈2: outstanding scientist, likely to be found only at the top universities or major research laboratories
• m≥3: a truly unique individual

(note the possible strong time-dependence of m during a person's career!)

Examples:

Group of physics Nobel prize winners from the last 20 years:
average h=41 (standard deviation 15), median h=35
average m=1.14 (stand.dev. 0.47) (49% with m<1)

Problem of cross-comparison between disciplines

It seems highly problematic to use the h-index for cross-comparison between different research disciplines or even subfields within a discipline because the average citation level may be largely different. What counts as a high number of citations in one field, may be seen as an only moderate number in another field. Obviously, this difference is then also reflected in the achievable h-index.

It is important to remember this, especially when comparing two or more individuals regardless of their research area. It is not advised to use the h-index as a measure in such a setting. This may be encountered in comparing candidates for a university faculty position, when the research area of the new faculty member was not well defined in the original advertisement. In such a case, the search committee has to determine the appropriate "citation scale" for the research areas of each candidate separately, before attempting a cross-comparison based on citation numbers (including the h-index).

This makes the h-index an unsuited tool for easy and immediate cross-comparison between research areas.